Why are some atomic nuclei radioactive?

If some nuclei are unstable and decay radioactively, then they cannot always have existed (otherwise, they would have decayed away) but must have been formed at some finite time in the past. Were they formed at (and have they been decaying since) the time the Universe formed (i.e. during the Big Bang, 13.6 billion years ago) or did they form by some process that operated prior to the time of formation of our solar system?

To understand why radioactivity exists and why radioactive nuclei are present in our solar system, it is necessary to understand the processes responsible for the formation of the chemical elements.

Synthesis of the chemical elements

Processes by which the chemical elements in the periodic table were formed are collectively called nucleosynthesis.

Nucleosynthesis is the creation of new nuclear species by fusion reactions.

The chemical elements were formed by two nucleosynthesis processes:

primordial nucleosynthesis operating during the Big Bang, and

stellar neucleosynthesis

Primordial nucleosynthesis

At t ≤1 sec after the Big Bang, the temperature was > 10^9°K and only photons, e-, p+, n plus decoupled neutrinos were present. No other nuclei could exist at this time because it was so hot that all nuclei would have been broken up by interactions with energetic photons.

Heavier nuclei could, in theory, be formed by energetic collisions and fusion of protons and neutrons once the temperature dropped. To make heavier elements by this means first requires formation of Deuterium (2H): D

Photo-disintegration of Deuterium ceased after the temperature dropped below T ~ 10^9°K, when the photons were no longer energetic enough to break Deuterium apart.

The lightest elements (He, Li) could form by Deuterium combining with protons and neutrons about 3 minutes after the Big Bang when the Universe had cooled enough but was still dense enough for nucleon interactions to occur. Their relative abundances have provided a successful predictive test of the Big Bang hypothesis.

However, there are two gaps (or bottlenecks) in primordial nucleosynthesis at atomic numbers A = 5 and 8 that stop the build-up of heavier nuclei; to go from 4He and 7Li to the next most massive species, it is necessary to add two neucleons simultaneously, as the next nuclei formed by addition of only a proton or a neutron are unstable and decay radioactively as rapidly as they form. So both a proton and a neutron must be added simultaneously to 4He to form the next heavier stable nuclei. The same is the case for 7Li; both a proton and a neutron must collide and combine simultaneously with a 7Li nucleus to form the next heavier stable nuclei. The first gap may be bridged by combining two heavier species, such as 3He and 4He. However, these reactions were improbable during primordial nucleosynthesis, due to the low abundance of these species.

Therefore, along the chain of progressively heavier nuclei built by primordial nucleosynthesis, by the addition of protons and neutrons to nuclei, only 1H, D, 3H, 3He, 4He and 7Li were formed in abundance by primordial nuclear reactions during the Big Bang. No further elements could form at these densities during primordial nucleosynthesis because nuclei at A = 5, 8 are unstable and decay rapidly after they are formed.

Where were the rest of the heavier elements made? They were made subsequently by fusion and neutron capture reactions within stars.

Stellar nucleosynthesis

Elements up to Fe were made largely by stellar fusion reactions, whereas the elements heavier than Fe were largely made by neutron capture reactions. These nuclear reactions can also be categorised as either equilibrium or explosive nucleosynthesis processes, referring to the rate of proton and neutron capture by nuclei with respect to the rate of their beta-decay. They are also referred to as either r- (for rapid), s- (for slow) and p- (for proton) nucleosynthesis processes.

Nucleosynthesis processes and production sites:

s-process: the capture of neutrons by atomic nuclei on a time scale that is much longer than the time required for the nuclei to decay via the emission of a beta particle. The s-process occurs by two main reactions which liberate neutrons in high enough abundance in thermally pulsing Asymptotic Giant Branch (TP-AGB) and Wolf-Rayet (high mass loss) stars.

r-process: the capture by atomic nuclei of neutrons on a rapid time scale so that regions of nuclear instability are bridged. The r-process occurs in novae and supernovae during star collapse.

During these nucleosynthesis processes, both stable and unstable (i.e. radioactive) nuclei are newly synthesised. It was during such nucleosynthesis events that our solar system’s radioactivity arose.

Formation of our solar system

The interstellar medium is the gas (99% by mass of ISM, comprising 90% H with the remainder mostly He), dust (≤µm irregular-shaped particles mostly of C and/or silicates), magnetic fields, and charged particles in the region between stars, comprising ~15% by mass of visible matter in the Milky Way.

The main mass contributors to the interstellar medium are:

thermally pulsing stars (red giants)

high mass loss (Wolf-Rayet) stars

novae

Much of the interstellar medium is thus derived from the ejected envelopes of pulsing or exploding stars. The interstellar medium provides the starting materials for our solar system.

Our solar system formed from the gravitational collapse of an interstellar cloud of gas and dust:

the solar nebula can be modelled as a large rotating disks of dust and gas, with mass transferred by gravity into its centre. As it contracted, heat could be radiated away but conservation of angular momentum requires the cloud to rotate faster. This caused a flattened “accretion disk” to form by centrifugal force

at some stage when the densities within the cloud core get high enough, fusion of H started and the proto-Sun formed, initially going through an unstable T-Tauri phase resulting in violent jets, flares, etc and the recycling of ejected material through the disk

elements began to condense from the nebula into fluffy dust grains, which collide, stick together and act as condensation nuclei, forming clumps of material

bipolar outflows, violent flares and intense radiation from the newly forming (T-Tauri phase) Sun restricted the condensation of volatiles (water, methane, ammonia) to the outer parts of the nebula (i.e. gas giants such as Jupiter and Saturn)

growth by accretion continued until bodies were large enough to gravitationally attract materials– then, runaway growth occurred to form small moon-sized objects called planetesimals

planetesimals swept up further material to form protoplanets, with a competing process of fragmentation breaking up to form small bodies following collisions with larger objects

gas and ice giants form before the inner (e.g. terrestrial) planets; the gravitational forces from these outer giants influenced the formation of the inner planets and asteroids

eventually only a few planet-sized objects remained, with the rest left as comets and asteroids

The solar system’s earliest materials formed within the solar nebula. Remnants of these are preserved in some meteorites.

Meteorites can be grouped into two types:

1. primitive

Carbonaceous Chondrite: similar in elemental composition to the Sun less volatiles, these meteorites contain small inclusions (i.e. CAI’s) that may have condensed directly from the solar nebula

may also contain chondrules; c. 1-mm spheres that are depleted of volatiles and were briefly melted to about 2000°K and cooled (in a region of high magnetic field)

chondrules commonly occur within an organic substrate that was not heated to the temperatures that made the chondrules

these meteorite types have not been inside a large molten body

2. differentiated

Iron: primarily iron and nickel; similar to type M asteroids and likely derived from the iron cores of fragmented differentiated planetesimals

Stony Iron: mixtures of iron and stony material like type S asteroids

Chondrite: most meteorites fall into this class; similar in composition to the mantles and crusts of the terrestrial planets

Achondrite: similar to terrestrial basalts; may have originated on Moon and Mars

parts of the interiors of planetesimals whose insides melted because they were large enough to retain heat (from radioactivity)

Some primitive meteorites (such as the Allende meteorite) contain Calcium and Aluminium rich Inclusions (CAI’s) and spherical structures called “chondrules”, typically ≤2 mm in diameter, of coarse crystals formed from the rapid cooling and solidification of a melt at about 1400°C. Large numbers of chondrules are found in all chondrites except for the CI group of carbonaceous chondrites. Chondrules are typically 0.5 to 2 mm in diameter and are usually composed of iron, aluminum, or magnesium silicates in the form of the minerals olivine and pyroxene, with smaller amounts of glass and iron-nickel. Together with Calcium and Aluminium rich Inclusions (CAI’s), which predate them by a few million years, they are among the oldest objects in the Solar System with an inferred age of about 4.57 billion years. They formed when dusty regions of the solar nebula were heated to very high temperatures, became molten, and then resolidified as tiny droplets.

Chondrules were formed in the disk of gas and dust surrounding the young Sun. Lightning and shock waves may have heated isolated regions of the disk, partially melting the dust. Chondrules may have formed when the innermost regions of the disk, heated by the Sun, could not cool quickly enough. Huge pockets of vaporized material rose to the surface of the disk, the Sun’s magnetic field lines grabbed them and flung them outward in a diffuse wind toward cooler regions. Particles between a millimeter and centimeter in size would eventually fall back onto the disk at planetary distances. Alternatively, enormous shock waves had enough energy not only to melt the disk, but also to completely vaporize dust surrounding the young Sun. A shock wave of dense, hot gas would hit a region of the disk and drag its material along. The friction of this event vaporized the dust, and then the hot gas of the wave kept temperatures warm enough so that the newly-formed droplets did not cool immediately.

The table below lists the inventory of observed radiogenic decay products of short-lived nuclides that have been detected in early solar system materials, principally CAI’s, chondrules and primitive (undifferentiated or chondritic) meteorites.

The presence of short-lived nuclides in the Solar System’s earliest condensates indicates that some proportion of the chemical elements of which our Solar System is composed were synthesised shortly before Solar System formation.

This nucleosynthesis event (or events), associated with the ejection of the outer envelope of a Thermally Pulsing Asymptotic Giant Branch (TP-AGB) or Wolf-Rayet star or a supernova event, may have triggered the collapse of a nearby an interstellar dust cloud to form our Solar System. As long-lived radioactive systems such as U-Pb and Pb-Pb have been used to date meteorites, and short-lived radioactivity provides a very accurate clock, this nucleosynthesis event can be precisely dated at 4571 million years ago. This date also corresponds to the time of formation of our Solar System.